Reflected BSDE of Wiener-Poisson type in Time-dependent Domains

TL;DR

This paper investigates multi-dimensional reflected backward stochastic differential equations driven by Wiener-Poisson processes within time-dependent domains, establishing existence and uniqueness of solutions with inward reflection.

Contribution

It introduces a novel framework for reflected BSDEs in time-dependent domains driven by Wiener-Poisson processes, proving fundamental existence and uniqueness results.

Findings

Existence and uniqueness of solutions for the reflected BSDEs.

Solutions reflect inward in time-dependent domains.

Framework applicable to multi-dimensional stochastic systems.

Abstract

In this paper we study multi-dimensional reflected backward stochastic differential equations driven by Wiener-Poisson type processes. We prove existence and uniqueness of solutions, with reflection in the inward spatial normal direction, in the setting of certain time-dependent domains.